Geodesic
Generalized Amalgams, With Applications to Fourier Transform
Canadian journal of mathematics, Tome 42 (1990) no. 3, pp. 395-409

Voir la notice de l'article provenant de la source Cambridge University Press

A recent survey article by J. Fournier and J. Stewart (Bull.AMS 13 (1985), 1-21) explains how amalgams of Lp with lq (as function spaces over any locally compact abelian group G) can be used as an effective tool for the treatment of various problems in harmonic analysis. The present article may be seen as a complement to this survey, indicating further advantages that arise if one works with generalized amalgams (introduced in 1980 under the name of Wiener-type spaces by the author [10]). The main difference between amalgams and these more general spaces is the fact that they allow a more precise description of the local behavior of functions (or distributions) by rather arbitrary norms and that the conditions on the global behavior (of the quantity obtained using that chosen local norm) is described in a way that includes both growth and integrability conditions (not only lq -summability).
DOI : 10.4153/CJM-1990-022-6
Mots-clés : 46E30, 43A15, 43A25, generalized amalgams, (generalized) Fourier transform, complex interpolation, Wiener type spaces, Hausdorff-Young inequality, p-localizable, ultra-distributions 
Feichtinger, Hans G. Generalized Amalgams, With Applications to Fourier Transform. Canadian journal of mathematics, Tome 42 (1990) no. 3, pp. 395-409. doi: 10.4153/CJM-1990-022-6
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